Nuprl Lemma : is-rec-class
∀[Info,T:Type].
∀G:es:EO+(Info) ⟶ E ⟶ bag(T). ∀F:es:EO+(Info) ⟶ e':E ⟶ T ⟶ {e:E| (e' <loc e)} ⟶ bag(T). ∀es:EO+(Info). ∀e:E.
(↑e ∈b RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])
⇐⇒ if e ∈b prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))
then let e' = prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))(e) in
#(F[es;e';RecClass(first e G[es;e]or next e after e' with value v F[es;e';v;e])(e');e]) = 1 ∈ ℤ
else #(G[es;e]) = 1 ∈ ℤ
fi )
Proof
Definitions occuring in Statement :
es-rec-class: es-rec-class,
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
let: let,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
es-rec-class: es-rec-class,
in-eclass: e ∈b X,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
prop: ℙ,
so_apply: x[s1;s2;s3;s4],
implies: P ⇒ Q,
uimplies: b supposing a,
top: Top,
eclass: EClass(A[eo; e]),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ,
ifthenelse: if b then t else f fi ,
let: let,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
eq_int: (i =z j),
true: True,
es-E-interface: E(X)
Latex:
\mforall{}[Info,T:Type].
\mforall{}G:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} bag(T). \mforall{}F:es:EO+(Info) {}\mrightarrow{} e':E {}\mrightarrow{} T {}\mrightarrow{} \{e:E| (e' <loc e)\} {}\mrightarrow{} bag(T).
\mforall{}es:EO+(Info). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])
\mLeftarrow{}{}\mRightarrow{} if e \mmember{}\msubb{} prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))
then let e' = prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))(e) in
\#(F[es;e';RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e');e])
= 1
else \#(G[es;e]) = 1
fi )
Date html generated:
2016_05_17-AM-06_29_37
Last ObjectModification:
2015_12_29-AM-00_39_42
Theory : event-ordering
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